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Exploring Zeros of Hermite- λ Matrix Polynomials: A Numerical Approach

Author

Listed:
  • Maryam Salem Alatawi

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Manoj Kumar

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Nusrat Raza

    (Mathematics Section, Women’s College, Aligarh Muslim University, Aligarh 202002, India)

  • Waseem Ahmad Khan

    (Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia)

Abstract

This article aims to introduce a set of hybrid matrix polynomials associated with λ -polynomials and explore their properties using a symbolic approach. The main outcomes of this study include the derivation of generating functions, series definitions, and differential equations for the newly introduced two-variable Hermite λ -matrix polynomials. Furthermore, we establish the quasi-monomiality property of these polynomials, derive summation formulae and integral representations, and examine the graphical representation and symmetric structure of their approximate zeros using computer-aided programs. Finally, this article concludes by introducing the idea of 1-variable Hermite λ matrix polynomials and their structure of zeros using a computer-aided program.

Suggested Citation

  • Maryam Salem Alatawi & Manoj Kumar & Nusrat Raza & Waseem Ahmad Khan, 2024. "Exploring Zeros of Hermite- λ Matrix Polynomials: A Numerical Approach," Mathematics, MDPI, vol. 12(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1497-:d:1392311
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